1. Suppose S is a sample space and A, B, and C are events in S, with P(A) > 0, P(B)>0,andP(C)>0,suchthatP(A∩B∩C)=P(A)·P(B)·P(C). Doesit follow that A and B are independent? note: why A and B must be independent, or give an example of a sample space S and events A, B, and C which meet the above conditions but for which A and B are dependent. 2. You are given 65 coins, 64 of which are fair and 1 of which has two heads. One coin is selected at random from the 65, and then tossed 6 times, coming up heads on every toss. What is the probability that the selected coin is the two-headed one? 3. A box contains three different types of disposable flashlights. Suppose that 20% of the flashlights in the box are of type A, 30% are of type B, and 50% are of type C. The probabilities that type A, type B, and type C flashlights will last over 100 hours of use are respectively 0.70, 0.40, and 0.30. a. What is the probability that a flashlight randomly chosen from the box will last over 100 hours of use? b. If a flashlight randomly chosen from the box lasted over 100 hours, what is the probability it was of type B?
1. Suppose S is a sample space and A, B, and C are
note: why A and B must be independent, or give an example of a sample space S and events A, B, and C which meet the above conditions but for which A and B are dependent.
2. You are given 65 coins, 64 of which are fair and 1 of which has two heads. One coin is selected at random from the 65, and then tossed 6 times, coming up heads on every toss. What is the
3. A box contains three different types of disposable flashlights. Suppose that 20% of the flashlights in the box are of type A, 30% are of type B, and 50% are of type C. The probabilities that type A, type B, and type C flashlights will last over 100 hours of use are respectively 0.70, 0.40, and 0.30.
a. What is the probability that a flashlight randomly chosen from the box will last over 100 hours of use?
b. If a flashlight randomly chosen from the box lasted over 100 hours, what is the probability it was of type B?
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